Chapter 6: Q3P (page 314)

$x y d x + x^{2} d y$ where C is as selected.

Short Answer

Expert verified

The integral will give the solution to be $\frac{14}{3}$ .

Step by step solution

Given information

The given equation is $x y d x + x^{2} d y,$ .

Definition of conservative force and scalar potential

A force is said to be conservative if $\nabla \times F = 0 .$ .

The scalar potential is independent of the path. The scalar potential is the sum of potential in all the 3 dimensions calculated separately.

The formula for the scalar potential is $W = \int F . d r$ .

Use Greens Theorem

Takethe values as mentioned below.

$P = x y Q = x^{2}$

Use the Green theorem.

$\oint x y d x + x^{2} d y, \iint x d y d x \int_{1}^{4} \int_{0}^{\sqrt{x}} x d y d x \int_{1}^{4} \sqrt{x d x} \frac{16}{3} - \frac{2}{3} \frac{14}{3}$

Hence the integral will give the solution to be $\frac{14}{3}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$x y d x + x^{2} d y$ where C is as selected.

Short Answer

Step by step solution

Given information

Definition of conservative force and scalar potential

Use Greens Theorem

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Astrophysics

Radiation

Nuclear Physics

Linear Momentum

Work Energy and Power

Study anywhere. Anytime. Across all devices.

xydx+x2dywhere C is as selected.

Short Answer

Step by step solution

Given information

Definition of conservative force and scalar potential

Use Greens Theorem

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Astrophysics

Radiation

Nuclear Physics

Linear Momentum

Work Energy and Power

Study anywhere. Anytime. Across all devices.

$x y d x + x^{2} d y$ where C is as selected.